The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
Generally, wavelet transform-based video data compression technique provides a solution to the blocking artifacts caused by conventional JPEG and other block-centered data processing methods, and is anticipated to be an excellent technique to provide the scalability and progressive transmission adapting to the transmission and storage medium atmosphere as it is being applied to the recent international standard JPEG2000 and Dirac, which is a video compression technique developed by British BBC.
A wavelet transform method is a method for recursively transforming image signals in a space region into those in a wavelet region using two one-dimensional filters, including a low band filter and a high band filter, in the horizontal and vertical directions of an input image. The wavelet transform method has a high energy concentration effect for flat image signals because it can provide sufficient directional vanishing moments in the horizontal and vertical directions, that is, the filtering directions.
Here, the directional vanishing moments refer to the state in which the energy of a wavelet transform coefficient is sufficiently collected in a low subband, thereby minimizing the transfer of energy in the direction of high band filtering.
There have been recently proposed discrete wavelet transform techniques that take the characteristics of images into consideration because it is recognized that a standard discrete wavelet transform scheme has a limitation on the production of a sufficient energy concentration effect along lines, edges and contours, that is, the intrinsic characteristics of image signals.
A fundamental reason for this trend will be described in more detail. In an existing discrete wavelet transform scheme, a wavelet transform is performed based on the filtering in both the horizontal and the vertical directions. Accordingly, in the case where the contours or edges of images are determined to have directions other than the two directions, sufficient directional vanishing moments cannot be provided for high-pass signals.    [Document 1] Roberto H. Bamberger, and Mark J. T. Smith (A Filter Bank for the Directional Decomposition of Images: Theory and Design, IEEE Trans. On Signal Processing, vol. 40, no. 4, pp. 882-893, April, 1992)    [Document 2] E. J. Candes (“Ridgelets: Theory and applications, Ph.D. dissertation, Dept. Statistics, Stanford Univ., Stanford, Calif., 1998)    [Document 3] E. J. Candes and D. L. Donoho (“Curvelets a surprisingly effective nonadaptive representation for objects with edges”, in Curve and Surface Fitting, A Choen, C. Rabut, L. L. Schmumaker, Eds. SaintMalo: Vanderbit University Press, 1999)
In order to solve the above-described problem, [Document 1] attempts to provide directional vanishing moments for a high-pass signal by using a filter bank having frequency responses for a variety of directions, not only the horizontal and vertical directions. [Document 2] and [Document 3] can significantly reduce the energy of a high band filter band by transforming two-dimensional continuous signals based on the characteristic information (lines and curves) of images.
[Document 4] Omer N. Gerek and A. Enis Cetin (“A 2-D Orientation-Adaptive Prediction Filter in Lifting Structures for Image Coding”, IEEE Trans. Image Processing, vol. 15, no. 1, pp. 106-111, January 2006)
However, the above-described methods are problematic in that they exact an excessive computational load because they cannot be independently implemented as a one-dimensional filter, as in existing wavelets.
In order to reduce the energy of the high band filter band while solving the problems as described above, [Document 4] proposes a prediction method using a 2-dimensional prediction filter of the edge direction based on the prediction-update lifting.
FIGS. 1 and 2 are block diagrams of a conventional lifting-based wavelet transform apparatus.
The conventional lifting-based wavelet transform apparatus includes an analysis unit 10 shown in FIG. 1 and an integration unit 20 shown in FIG. 2. The analysis unit 10 transforms an input signal into a wavelet coefficient, and the integration unit 20 transforms the wavelet coefficient into a reconstruction signal.
The analysis unit 10 includes a decomposer 11, a predictor 13, and an updater 15 as shown in FIG. 1, and the integration unit 20 includes an updater 21, a predictor 23, and a composition unit 25 as shown in FIG. 2.
In one-dimensional wavelet transform, the decomposer 11 decomposes a one-dimensional signal into even and odd polyphase samples, and the predictor 13 predicts the plurality of odd polyphase samples based on a plurality of surrounding even polyphase samples, and subtracts the predicted value from the odd polyphase samples, thereby calculating the residual polyphase samples.
Finally, the updater 15 predicts even polyphase samples based on the calculated residual polyphase samples and adds the predicted value to the even polyphase samples, thereby creating updated polyphase samples.
In this case, if a filter having a form specific to prediction and update is used, the updated even polyphase samples become a wavelet coefficient that has passed through a low band filter and the predicted odd polyphase samples (residual polyphase samples) become a wavelet coefficient that has passed through a high band filter. The wavelet coefficients can be reconstructed to the original signal again by the integration unit 20 of FIG. 2.
The lifting based wavelet as described above can be extended and applied to a two-dimensional signal. That is, a wavelet transform is performed on a two-dimensional signal in such a way as to perform decomposition/prediction/update on the two-dimensional signal in the vertical direction and then perform decomposition/prediction/update on created updated polyphase samples and residual polyphase samples again in the horizontal direction.
While the conventional lifting-based wavelet transform apparatus employs a lifting scheme in which the wavelet is implemented in the order of division, prediction, and update as described above, the wavelet is performed in the sequence of division, update, and prediction in the prediction-update lifting scheme.
[Document 4] has enabled a removal of energy in a high band more than the simple wavelet of a two-dimensional signal by employing a directional prediction in the prediction-update lifting based wavelet. That is to say, [Document 4] has tried to reduce the energy of the high band based on the prediction-update lifting based wavelet. The method of [Document 4] will now be described below.
Each one-dimensional wavelet is decomposed into odd and even polyphase samples along the horizontal direction. Then, the even polyphase samples are updated in the horizontal direction by using the odd polyphase samples. That is, the even polyphase samples are updated by the odd polyphase samples located at the left and right of the even polyphase samples. Then, the odd polyphase samples are predicted by adjacent updated even polyphase samples. In order to enhance the efficiency of the prediction, not only the even polyphase samples located in the horizontal direction of the odd polyphase samples but also the even polyphase samples located in the diagonal direction of the odd polyphase samples may be used in the prediction. In other words, if the edge is located in the diagonal direction, a prediction using even polyphase samples located in the diagonal direction (+45 degrees, −45 degrees) may be superior to a prediction using even polyphase samples located in the left and right sides of the odd polyphase samples. Therefore, although the prediction is performed only in the horizontal direction (0 degrees) in the conventional method, the prediction is performed in three directions including +45 degrees, 0 degrees, and −45 degrees in the method of [Document 4].
When the lifting in the horizontal direction is complete, the lifting is performed again in the vertical direction according to the method as described above.
The reason why the updating is performed only in the horizontal or vertical direction is in order to properly remove aliasing of the updated even polyphase samples since the updated even polyphase samples should recursively perform the wavelet decomposition again.
[Document 4] effectively removes high band energy by performing the prediction in consideration of the direction of the edges. However, it is problematic in that, when the prediction direction is a diagonal direction, the prediction is performed without using the information of the updated even polyphase samples containing the information of the odd polyphase samples to be predicted. Further, since the directions are limited to only +45 degrees, −45 degrees, and 0 degrees, it is impossible to process all of the various directions of the edges, which degrades the efficiency.